IEEE Power & Energy Society
November 2014
TECHNICAL REPORT
PES-TR16
Transient Limiting
Inductor Applications in
Shunt Capacitor Banks
PREPARED BY THE
Transmission & Distribution Committee
Capacitor Subcommittee with input from
The Switchgear Committee
Task Force on Inductor Applications in Shunt Capacitors
© IEEE 2014 The Institute of Electrical and Electronic Engineers, Inc.
No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher.
THIS PAGE LEFT BLANK INTENTIONALLY
ii
TASK FORCE ON
Inductor Applications in SHUNT CAPACITORS
Chair: ROY ALEXANDER
Main Authors:
Roy Alexander
Lucas Collette
Tom Grebe
Halim Malaj
Joe Meisner
Other Members and Contributors
Stan Billings
Gilbert Carmona
Bill Chai
Vince Chiodo
Denis Dufournet
Victor Hermosillo
Helmut Heiermeir
David Lemmerman
Dan Luke
Tom Mulchahy
Jeffrey Nelson
Shree Sathe
Richard Sevigny
Biswajit Singh
Jim vandeList
Xi Zhu
Arben Bufi
Stephen Cary
K.S. Chan
Roggero Ciofani
Bruce English
John Harder
Bjorn Lofgren
Paul Marken
Mark McVey
Pratap Mysore
Jon Rogers
Carl Schuetz
Sushil Shinde
Vernon Toups
Dong Sun Yoon
iii
ACKNOWLEDGMENTS (Optional)
The Task Force is truly grateful for the support of our sponsoring subcommittee and
committees.
iv
CONTENTS
Contents
1. INTRODUCTION ...........................................................................................................1
2. FIXED SERIES INDUCTORS (TRANSIENT LIMITING INDUCTORS) ..................2
2.1 Uses and Sizing ...............................................................................................................2
2.1.1
Limiting Inrush/Outrush Transients............................................................................................... 2
2.2 Drawbacks of Installing TLIs ..........................................................................................7
2.2.1
2.2.2
2.2.3
Transient Recovery Voltages ......................................................................................................... 7
Tuning ........................................................................................................................................... 8
Losses/Loss Evaluation and Initial Cost ...................................................................................... 10
2.3 Where to Locate the Fixed Inductors ............................................................................11
2.4 TRV Delay Capacitors for the TLI................................................................................11
2.4.1
2.4.2
Location of TRV Delay Capacitors ............................................................................................. 13
Sizing TRV Delay Capacitors ..................................................................................................... 14
3. REFERENCES ..............................................................................................................14
APPENDIX A .....................................................................................................................17
A.1
Overview of Capacitor Bank Switching Transients...............................................17
A.2
Isolated (Single) Capacitor Bank Switching Transients ........................................17
A.3
Back-to-Back Capacitor Bank Switching Transients ............................................19
A.4
Transient Outrush Currents during Nearby Faults .................................................21
A.5
Transient Overvoltages from Capacitor Bank De-Energizing and Restrikes ........27
APPENDIX B .....................................................................................................................31
B.1
Capacitor Bank Switching Transient Mitigation Methods ....................................31
B.2
Pre-Insertion Devices .............................................................................................31
B.3
Controlled Closing (Point on Wave Closing Control) ...........................................34
B.4
Surge Arresters.......................................................................................................35
B.4.1
B.4.2
B.4.3
B.4.4
Uses ............................................................................................................................................. 35
Drawbacks ................................................................................................................................... 37
Where in the Circuit to Locate the Surge Arresters ..................................................................... 37
How to Size the Surge Arresters .................................................................................................. 38
APPENDIX C .....................................................................................................................39
Example 230kV Capacitor Bank TLI Study .......................................................................39
C.1
Terminology...........................................................................................................39
C.2
Introduction ............................................................................................................39
C.3
Equations for Calculating the Outrush Current .....................................................40
C.4
Outrush Current Calculation for Example Capacitor Bank ...................................41
APPENDIX D .....................................................................................................................43
Capacitor Bank TLI Sizing and Application Guide Including TRV Mitigation ................43
D.1
Terminology...........................................................................................................43
D.2
Introduction ............................................................................................................44
v
D.3
Proposed method for determining Capacitive Inrush (outrush) capability of circuit
breakers .........................................................................................................................45
D.4
Vacuum Breaker Example .....................................................................................46
D.5
Line Oil Breaker Example and TRV Calculations ................................................47
vi
1.
INTRODUCTION
Fixed Inductors are often used in shunt capacitor installations in series with each
phase of a capacitor bank. The inductors primary purpose is to limit transient
currents during switching (inrush) or close in faults (outrush). In wye connected
banks inductors have been placed between the bus and the capacitor switching
device, between the capacitor switching device and the capacitor, or between the
neutral end of each phase of the capacitor and the neutral point as shown in Figure
1.
Switching Transient limiting
Device
inductor (TLI)
Transient limiting
inductor (TLI)
Switching
Device
Capacitor
bank
Capacitor
bank
Switching
Device
Capacitor
bank
Transient limiting
inductor (TLI)
Figure 1. Illustration of example transient limiting inductor installations.
Since the primary purpose of these fixed inductors is to limit transient currents
associated with the capacitor bank, we name them: “Transient Limiting Inductors”
(TLIs). These are fixed series inductors, not to be confused with “pre-insertion
inductors” supplied with some capacitor switching devices, which are only
temporarily in the circuit during a closing operation.
In the past 10 – 15 years capacitor bank faults have arisen where the capacitor was
shorted out and the fault impedance was the TLI in series with the system back – up
impedance. This situation gives rise to a Transient Recovery voltage (TRV) that is
unmanageable by many circuit breakers, resulting in the circuit breaker failing to
interrupt. Some kind of TRV mitigation is required to prevent this.
Some thought that by placing the TLIs in the neutral end of the capacitor bank, that
the above failure scenario was eliminated. Placing the TLI in the neutral end does
result in the TLI being bypassed in two fault scenarios (capacitor terminal to ground
1
or phase to phase) but it doesn’t help for the possible fault which is shorting of the
capacitor bank itself, phase to neutral.
This Committee Technical Report was written in response to a great amount of
confusion in the Power industry surrounding the application of TLIs in shunt
capacitor banks.
2.
FIXED SERIES
INDUCTORS)
2.1
INDUCTORS
(TRANSIENT
LIMITING
Uses and Sizing
2.1.1 Limiting Inrush/Outrush Transients
Fixed Transient Limiting Inductors (TLIs) often called current limiting reactors
(CLRs) have been used successfully to limit inrush currents during back-to-back
capacitor bank switching. Typically, the value of these inductors is approximately
several hundred microhenries. In addition, inductors for fault outrush current
control may be applied, and are typically 0.5 - 2.0 mH. Previous research indicates,
however, that these fixed inductors do not provide appreciable transient
overvoltage reduction, unless they are very large. Very large inductors convert the
capacitor bank to a true harmonic filter branch (often 13th harmonic or lower).
2.1.1.1
How to Size the Fixed Inductors
Sizing the fixed inductors should be done in such a way that at a minimum the
inrush and outrush currents through the switching device will not exceed the
device’s capability. Historically, the product of the current peak and frequency (I x f
limits) defined in IEEE C37.06 standards [7] have been used to size transient
limiting inductors for shunt capacitor banks. C37.06-2009 [6] no longer requires
outrush inductors for circuit breakers having a Class C1 or C2 capacitance current
rating as long as the peak current is below 2.6 x the short-circuit rating of the
breaker.
There has been debate that the I x f limits published in IEEE standards are incorrect
and have resulted in incorrect sizing of inductors when limiting the I x f to within
the switching device’s “supposed” capability. SF6 and vacuum switching devices are
not particularly frequency sensitive so their limits could be better expressed with
peak current magnitude or peak current and duration.
Beyond concerns over the limitations of switching devices, TLIs can be sized to limit
transient ground rise and control circuit coupling.
2
2.1.1.2
Switchgear Limits
Through 2014, IEEE standards provide a value of peak rated current and frequency
of transients exposed to inrush currents from capacitor banks. For circuit breakers
with a Class C1 or C2 rating IEEE Std. C37.06-2009 [6] provides a preferred rating,
an Alternate 1 rating, an Alternate 2 and an Alternate 3 rating. The Alternate 2 and
3 ratings are an attempt to recognize the larger inrush capabilities of SF6 circuit
breakers. The Alternate 1 ratings are to limit inrush currents to 6 kA for vacuum
circuit breakers to maintain their C2 capabilities. For Class C0 circuit breakers, the
transient inrush peak current on closing is to be less than 1.41 times the rated shortcircuit current or 50 kA (whichever is less) and the product of the inrush current
peak and frequency shall not exceed 2x107 A-Hz. IEEE Std C37.06-2009 also
provides commentary that for Class C1 or C2 circuit breakers exposed to outrush
currents during fault conditions, the breaker should be expected to handle peak
currents up to the close and latch rating of the circuit breaker twice during its life
time without requiring maintenance of the contacts.
2.1.1.3
Capacitor Current Inrush limitations of Switchgear
Interest is rising in understanding the physics behind the inrush/outrush current
limitations of switching devices. In a capacitive discharge, there is a fixed amount of
energy available. The amount depends on the energy stored in capacitance just
before a switching event, and the amount stored in the involved capacitors
immediately after the event. For example, in a fault outrush event, all the energy
stored in the capacitor banks is dissipated. In a back to back switching event, some
of the initial stored energy is transferred to the previously un-energized capacitors,
the remainder is dissipated.
The dissipated stored energy is split amongst:
Resistive losses in the circuit external to the switching device
Arc losses in the switching device:
•
•
•
Contact erosion
Heating of arc gasses
Shock waves
The shock wave energy does appear to be related to di/dt, however it cannot exceed
the energy available. There is a threshold energy below which shock waves will not
be damaging.
Arcs in oil are particularly effective at converting capacitive discharge into
destructive shockwave shock wave energy. Arcs in Air and SF6 create shock waves,
but with much lower destructive energy than in oil, perhaps several orders of
magnitude less.
Problems with the pre - 2014 di/dt method and limits are as follows:
3
•
•
•
•
•
A minimum threshold energy is not considered.
It derives from oil interrupter technology which is particularly shock wave
sensitive.
It does not account for non-oil technologies which have limitations other
than shock waves.
It has resulted in users installing series TLIs for SF6 circuit breakers which
may be unnecessary; and for oil circuit breakers perhaps larger than needed.
Adding TLIs can result in TRV difficulties for SF6 and air circuit breakers
which would not exist without the TLIs.
The following is a practical example of the inappropriateness of the di/dt (Ixf)
method/limits when capacitors are small:
Consider a 245 kV installation with two 5 nF CCVTs (or TRV shaping capacitors) on
each side of a circuit breaker with 20 m (20 µH inductance) of buswork (and return
path) between the CCVTs (or TRV shaping capacitors) as shown in Figure 2.
245 kV Bus
5 nF
CCVT
Circuit breaker in
closed position
20 m of buswork
(20 microhenries)
Circuit breaker closes
and energizes 2nd CCVT
Circuit breaker in
open position
5 nF
CCVT
Figure 2. Example case with closing
a circuit breaker between two 5 nF CCVTs.
The peak and frequency of the inrush current through the breaker could be
calculated as follows:
Frequency =
Peak =
1
2π LC
245000x 2 3
LC
=
1
−6
(
2π 20x10 x 5x10
=
−9
245000x 2 3
(
20x10 −6 5x10 −9 2
2
)
)
= 712 kHz
= 2.2 kA
I x F = 712 kHz x 2.2 kA = 1566 kAkHz (157x10 7 A − Hz)
4
(1)
This I x f is over 78 times the formerly used limit of 2 x 107 A-Hz, and over 18 times
the 8.5 x 107 A-Hz used for “definite purpose” breakers. Similar installations do
exist in service and are known not to cause trouble for even oil circuit breakers.
The energy available is ½ the energy stored in one capacitor. If the breaker is closed
with one capacitor charged to the crest voltage and the other discharged, the
starting energy is ½ CV2. At the end of the discharge, each capacitor will be charged
to ½ of the Peak voltage. The ending energy is ½ C (V/2)2 + ½ C (V/2)2 = C(V/2)2 =
¼ CV2. Half of the initial energy is stored and the other half is dissipated. The
available energy is then ¼ CV2. Plugging in: 5 nF/4 x (200 kV)2 =50 Joules. Only a
fraction of this energy can be converted into shock wave energy
For the same case only with 13 nF CCVTs, the following would be the peak and
frequency:
Frequency =
Peak =
1
2π LC
245000x 2 3
LC
1
=
−6
(
2π 20x10 x 13x10
=
−9
245000x 2 3
(
20x10 −6 13x10 −9 2
2
)
)
= 441 kHz
= 3.61 kA
I x F = 712 kHz x 2.2 kA = 1567 kAkHz (157x10 7 A − Hz)
(2)
Since the peak voltage is the same, the energy available is directly proportional to
the ratio of the capacitances used in the 2 examples, i.e. 13 nF/5 nF = 2.6 so the
available energy is 2.6 x 50 J = 130 J.
As shown in the two examples above, the I x f product for both the cases with the 5
nF CCVTs and the 13 nF CCVTs is identical (except for round-off error) even though
the ratio of capacitance and energy is more than double between the two cases. .
From lack of in-service trouble, we could conclude that 50 J and probably 130 J of
available energy may be below the threshold for damage.
Since in a capacitive discharge circuit, the di/dt reduces to U/L, the value of the
capacitance doesn’t enter into the calculation of I x f.
A paper is being prepared: “The Impact of Capacitor Inrush/Outrush Currents on
Switchgear – Shock Wave and Contact Erosion”. The methodology is based on
fundamental arc physics and some simple laboratory tests. The purpose of the
paper is to demonstrate that typical capacitor inrush and outrush currents are not a
problem for SF6 circuit breakers. The concern on inrush is limited to contact wear.
TLIs may not be needed for such devices. Vacuum circuit breakers may still require
TLIs in capacitor applications mainly to insure they maintain their C1 or C2 restrike
performance.
5
2.1.1.4
Transient Ground Rise
Fast transients creating high di/dt, due to capacitor fault outrush and back to back
capacitor switching inrush currents, can result in transient ground rise if these
currents are permitted to flow in the ground grid. For capacitor bank installations
with high inrush and outrush currents, careful ground grid design and proper
grounding practices can be used to mitigate excessive transient ground potential
rise. Single point grounding is one method which can be used to eliminate most of
the ground grid currents from back to back capacitor switching. Single point
grounding is a technique where all neutrals of all capacitor banks at a given voltage
in a substation are connected together and grounded at a single point. Single point
grounding mitigates the impact of back to back switching transients as far as ground
rise is concerned, but doesn’t eliminate transient ground rise for a fault outrush
condition. However, back to back transients are frequent events and fault outrush is
usually far less frequent. The operational aspects of transient ground rise can also
be mitigated by connecting low voltage MOVs to local ground from low voltage
circuits that are grounded outside the capacitor bank area. Other grounding
practices such as peninsula grounding and direct neutral grounding [2] have also
been successfully used in shunt capacitor bank installations.
TLIs can be used to reduce the di/dt and hence transient ground rise potentials
between capacitor area grounds and remote grounds. If TLIs are installed to reduce
transient ground rise, a detailed study is needed to determine how much the di/dt
needs to be reduced for proper operation. Although this is a complex issue, it is
often safe to assume that if the di/dt is reduced to the design short-circuit di/dt that
would be low enough. Usually that requires a very large inductance TLI comparable
to making the capacitor banks harmonic filters.
2.1.1.5
Control System Coupling
Induction into control systems can be minimized by proper shielding of control
cables with the shields grounded at both ends and at critical points in the run. Also
the routing of the control circuits must not compromise any special grounding
design such as single point grounding or peninsular grounding. To minimize
induction, the control circuits should not be run closely parallel to (i.e. underneath
and in the same orientation as) phase conductors, or single point grounding
conductors carrying capacitor related transient currents.
2.1.1.6
CT/LC Secondary Voltage
CT secondaries can be protected by appropriate MOVs preferably across each full
secondary winding, and from the neutral point of the CT circuit to local ground. The
MOVs need to be located as close as possible to the CT windings preferably in the CT
secondary terminal box.
6
2.1.1.7
Other Limitations
All portions of the primary circuit through which inrush and outrush currents may
flow must be capable of withstanding the peak currents expected. All ground
connections should be as direct as possible and run so as to minimize extraneous
ground wire inductance.
2.2
Drawbacks of Installing TLIs
2.2.1 Transient Recovery Voltages
When transient limiting inductors are installed for capacitor banks to limit inrush
and outrush currents there is a potential that if a fault occurs in such a way that the
inductor (transient limiting inductor) limits the fault current interrupted by the
switching device (with minimal capacitance between the breaker and inductor)
excessive TRV’s can be imposed on the circuit breaker. Refer to Figure 3 for an
illustration of a reactor-limited fault for three example capacitor bank
configurations. For each of the examples in Figure 3, a transient recovery voltage
will be imposed on the circuit breaker that will often exceed standard circuit
breaker TRV ratings [9] if no mitigation is installed to limit the transient recovery
voltage component driven by the natural frequency of the inductor. This
phenomenon is somewhat similar to a short line fault. Both cases are covered in [9].
Circuit
breaker
Transient limiting Circuit
breaker
inductor (TLI)
Transient limiting
inductor (TLI)
Capacitor
bank
Fault phase-toground or
phase-to-phase
Fault phase-toground or
phase-to-phase
Example with circuit breaker before TLI
Capacitor
bank
Example with circuit breaker after TLI
Circuit
breaker
Fault across
capacitor bank
Capacitor
bank
Transient limiting
inductor (TLI)
Example with TLI in the capacitor bank neutral
Figure 3. Example capacitor bank configurations with a TLI-limited fault.
7
2.2.2 Tuning
Installing a TLI in a capacitor bank will create a series resonant circuit. One needs to
be aware of existing harmonics (usually very high order) that might excite this
resonant circuit and produce unwanted loading on the capacitor and TLI.
A simple single frequency filter consists of a shunt capacitor with a fixed inductance
in series. This may be the intended design or may simply be a side effect of adding a
transient limiting inductor to a capacitor bank installation. An example circuit is
shown in Figure 4.
Figure 4. Simple harmonic filter.
Typically only odd harmonics propagate through the electric system. These are
divided into positive (1,7,13), negative (5,11,17), and zero (3,9,15) sequence
harmonics. The zero sequence or triplen harmonics will only circulate through a
grounded system. Thus, single frequency filter banks for positive and negative
sequence harmonics are typically operated wye-ungrounded, while filter banks for
zero sequence harmonics should be operated wye-grounded.
This section provides a very basic look at simplified single-frequency filter banks,
specifically for capacitor bank design and effects of tuning. IEEE 1531 [3] should be
consulted for a more in depth treatment of harmonic filters.
2.2.2.1
Single Frequency Tuning
A single frequency filter is typically tuned to a particular harmonic current (n). At
the tuning frequency the impedance of the bank is minimized allowing the specified
harmonic current to flow. The following equation demonstrates how the inductance
and capacitance are tuned to the harmonic number.
nωL −
1
nωC
=0
(3)
8
Where:
n = harmonic #
ω = angular frequency = 2πf
L = total inductance in each leg (H)
C = total capacitance in each leg (F)
As shown in the equation above, the circuit inductance and capacitance is
completely compensated. Only the resistance of the circuit is left to limit the flow of
harmonic current.
A filter may also be tuned to a non-integer number. For example, a harmonic filter
tuned to # 5.2 is designed to eliminate most of the 5th harmonic current and will
slightly reduce the 7th harmonic current as well. A shunt bank should never be tuned
to the fundamental frequency, as the resulting fully compensated circuit would
simulate a fault.
2.2.2.2
Avoiding Tuning Frequencies
Most capacitor banks are designed using standardized capacitor units. Thus, it is
necessary to verify that the installation is not tuned unintentionally. If the fixed
shunt bank capacitance is known, the fixed inductance value can be found for a
specified harmonic (n).
L=
1
n ω2C
(4)
2
In order to avoid most tuned harmonic points. The capacitor bank can be tuned well
beyond any harmonics that are present on the system. A conservative approach
would be to ensure the reactor is tuned above the 13th harmonic. Solving the
equation (4) for n ≥ 15 would provide a maximum inductance value. Some inverters
produce non integer harmonics of a higher order around 23rd harmonic or higher. A
detailed study may be required to see if it is necessary to avoid tuning to those
frequencies.
2.2.2.3
Tuned Filter Bank Design
If the reactor is purposefully tuned to a specific frequency, then the whole filter
installation must be further examined to ensure that there is adequate margin to
accommodate additional harmonic currents. (See IEEE 1531 [3])
The capacitance can be found using the desired Mvar output of the bank (Q) at the
system nominal voltage (VSY).
Q (n 2 - 1)
C= 2
VSY ω n 2
(5)
9
Where:
Q = rated filter power (Mvar)
VSY = phase-to-phase bus voltage (kV)
System studies or measurements should be performed to find the maximum amount
of harmonic current (In). The 60Hz thermal equivalent current circulating in each
leg can be found by summing the harmonic and fundamental currents:
I EQ = I12 + I 2n
(6)
Where:
IEQ = Equivalent 60Hz rms Current (A)
I1 = Fundamental rms Bank Current (A)
In = Maximum rms nth Harmonic Current (A)
Multiple iterations may be required before the best capacitance and inductance
values are found. An economic design would dictate that standardized capacitor
cans are used while the fixed inductor would be custom built.
After determining the final capacitance and inductance values, the equipment
ratings should be verified using the following equations:
IL = fL × I
(7)
Where:
VC =
IL = Rated 60Hz Inductor Current (A)
fL = Current Margin, typ. ≥ 1.1
fC × I
ωC
Where:
(8)
VC = Rated Capacitor Bank Voltage (V)
fC = Voltage Margin, typ. ≥ 1.1
2.2.3 Losses/Loss Evaluation and Initial Cost
Perhaps the most obvious drawback to use of TLIs is their initial cost.
Depending on the design details, there is the cost of the TLI itself, the possible cost
of TRV mitigation and the cost of accommodating the TLI. It may be possible to
mount the TLI on the Capacitor equipment rack. The mechanical loading needs to
be considered in the rack design, particularly the wind loading. For Capacitor bank
10
installations higher than 245 kV, the TLI will need its own structure, foundation and
insulators.
Secondly, the TLI will add power losses due to its insertion resistance.
If the TLI has a large inductance, there will be a considerable voltage rise across it,
possibly necessitating a higher voltage rated capacitor bank. The TLI will actually
increase the VAR output of the capacitor bank due to the voltage rise across it
overcoming the series VAR loss.
2.3
Where to Locate the Fixed Inductors
When installing transient limiting inductors (TLIs) for controlling inrush and
outrush currents, the inductors need to be in series with each phase of the capacitor
bank. The location of the inductor relative to the circuit breakers and capacitor
bank (i.e., on the system or capacitor side of the switching device or on the system
side or neutral side of the capacitor bank) does not matter in terms of limiting
inrush and outrush currents as long as they are installed on each phase and in series
with the capacitor bank. For example, if the three configurations shown in Figure
1.1 have the same size capacitor bank and TLIs then the inrush and outrush currents
for each configuration will be similar. Note that technically it is also possible to
distribute the transient limiting inductors throughout the capacitor bank (small
inductors for each capacitor unit). This has usually proven to be a cost prohibitive
solution. When tank type capacitors are used, individual inductors can more easily
be accommodated in each tank and this is an effective solution.
Since about 2005 many have advocated installing the TLIs in the neutral end of the
capacitor bank. A disadvantage is that the neutral end of the capacitor then must be
insulated to support the full phase to ground voltage during an energizing condition
and 2 x the phase to ground voltage for a restrike condition. For banks of higher
voltage rating than 145 kV this can be prohibitive. It requires a taller capacitor
block, and imposes higher foundation loads. Also, the additional neutral end
insulation causes the fault probability to shift slightly away from a line end terminal
to ground fault towards a line to neutral fault. This somewhat defeats the initial
thinking of placing the TLIs at the neutral end. The above, concerns do not apply for
ungrounded neutral capacitor banks. The consensus of the WG is that a neutral end
location of the TLI can work, but it is not a preferred location. The use of a reduced
end to end BIL with arrester protection for the TLI is applicable for any TLI location
and not peculiar to the neutral end location.
2.4
TRV Delay Capacitors for the TLI
The installation of TLIs in capacitor bank applications limit the rate of rise of
current, as explained in the paragraphs above, resulting in softening the impact of
back to back switching by limiting current inrush and outrush. However, the
arrangement changes the configuration of the circuit to the extent that it can affect
11
the circuit breaker performance due to the rate of rise of the transient recovery
voltage during the circuit breaker attempt to clear the faults in the capacitor bank
itself or between the capacitor bank and the inductor (see Figure 5 below).
Figure 5. Typical TLI installation in capacitor bank applications.
When the circuit breaker interrupts the fault, the voltage potential across its
contacts (TRV), equals the vector difference of the voltages on the line and load side
of the opened circuit breaker contacts. As the voltage on the system (bus) side of
the circuit breaker returns to the normal frequency and the systems’ voltage rating,
the voltage on the load side oscillates at a high frequency determined by the values
of the TLI inductance (L) and the equivalent stray capacitance on the load side of the
inductor (Cstray). The voltage on the load side can be estimated as follows:
VL = I SC x ωL
(9)
Where:
VL = peak TLI voltage in kilovolts
Isc = peak short-circuit current in kilo amperes
L = inductance of the transient limiting inductor
The frequency of the oscillation is given by the equation:
f=
1
2π LC stray
Where:
(10)
f = frequency of oscillation (in Hertz)
Cstray = stray capacitance on the inductor side of the circuit breaker
The capacitance, Cstray, consists of the equivalent stray capacitance of; the inductor,
the bus between the inductor and the circuit breaker including the phase to ground
capacitance of the load side of the circuit breaker and the bus from the inductor to
the point of fault. This capacitance typically sums to a small value of few hundreds of
12
picofarads, yielding to a frequency of oscillation of hundreds of kilohertz and, as a
result, leading to a very high Rate of Rise of Recovery Voltage (RRRV) across the
circuit breaker contacts. This phenomenon is known and such events have occurred
in the past on different voltage levels throughout the utility industry and have been
documented in numerous IEEE papers.
As equation 10 above suggests, the increase of Cstray would decrease the frequency
of the oscillation. The increase of Cstray also decreases the RRRV of the TRV since the
voltage across a capacitor is given by:
V=
Q
C
(11)
Where:
Q = is the capacitor charge
From the formula above the voltage rate of change is:
dV 1 dQ I
=
=
dt C dt C
Where:
(12)
I = is the current flowing through the capacitor. Higher capacitance results in
slowing the voltage rise
Practical solutions to limit the TRV for these applications have been found by adding
surge capacitors on the load side of the circuit breaker. The main locations for these
capacitors are:
•
•
Line to ground between the circuit breaker and TLI or
Across the TLI
2.4.1 Location of TRV Delay Capacitors
2.4.1.1
Line to Ground
A line to ground location can be used but it will require a fully insulated capacitor
that will be under normal full voltage stress.
2.4.1.2
Across TLI
This may be a more difficult mounting position but here the capacitor will only see
significant voltage during transient events. One needs to calculate the tuning point
of the TLI and its parallel capacitor to make sure that a higher order harmonic is not
inadvertently magnified.
13
2.4.2 Sizing TRV Delay Capacitors
2.4.2.1
Voltage Rating
The voltage rating depends on the location. For line to ground connections the full
system voltage rating will be required as well as full system BIL.
For a capacitor across the TLI, the voltage rating needs to be high enough to
withstand the peak voltage during transient conditions including lightning
transients, and breaker restrike events. The normal (steady state) voltage across
the capacitor will be usually < 5% of the system voltage.
It is also possible to use an MOV across the TLI and capacitor to clamp the voltage
and allow lower TLI and capacitor Insulation values. One must be careful that the
MOV clamping voltage is not so low that it shorts out the TLI during inrush/outrush
events.
2.4.2.2
Capacitance
The capacitance value will need to be determined by a TRV study for the circuit
breaker. Capacitance is required to reduce the slope of the TRV from a fault where
the TLI would be a major contributor to the fast portion of the TRV.
Normally one would look at the case where the capacitor bank is shorted and the
fault impedance is the TLI and the system back up impedance. This applies
regardless of where the TLI is located in the capacitor circuit. TLIs in the neutral end
of a capacitor bank are not exempt from this.
3.
REFERENCES
[1]
IEEE Standard for Shunt Power Capacitors, IEEE Std. 18-2012, February
2013, IEEE, ISBN: 978-0-7381-8155-4.
[3]
IEEE Guide for Application and Specification of Harmonic Filters, IEEE Std.
1531-2003, December 2003 (Reaffirmed 2009), IEEE, ISBN: 0-7381-3719-7.
[2]
[4]
[5]
[6]
IEEE Guide for the Application of Shunt Power Capacitors, IEEE Std. 10362010, January 2011, IEEE, ISBN: 978-0-7381-6492-2.
IEEE Guide for the Application of Metal-Oxide Surge Arresters for
Alternating-Current Systems, IEEE Std. C62.22-2009, July 2009, IEEE, ISBN:
978-0-7381-5936-2.
IEEE Standard Rating Structure for AC High-Voltage Circuit Breakers, IEEE
Std. C37.04-1999, December 1999, IEEE, ISBN: 0-7381-1781-1.
IEEE Standard for AC High-Voltage Circuit Breakers Rated on a Symmetrical
Current Basis - Preferred Ratings and Related Required Capabilities for
14
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
Voltages Above 1000 V, IEEE Std. C37.06-2009, November 2009, IEEE, ISBN:
978-0-7381-6079-5.
American National Standard AC High-Voltage Circuit Breakers Rated on a
Symmetrical Current Basis- Preferred Ratings and Related Required
Capabilities, ANSI Std. C37.06-2000, May 2000, IEEE, ISBN: 0-7381-3595-X.
American National Standard Guide for High-Voltage Circuit Breakers Rated
on Symmetrical Current Basis Designated-Definite Purpose for Fast
Transient Recovery Voltage Rise Times, IEEE C37.06.1-2000, March 2000,
IEEE, ISBN: 0-7381-3597-6.
IEEE guide for the Application of Transient Recovery Voltage for AC HighVoltage Circuit Breakers C37.011-2011 November 2011 IEEE, ISBN 978-07381-7141-8
IEEE Application Guide for Capacitance Current Switching for AC HighVoltage Circuit Breakers, IEEE Std. C37.012-2014, May 2014, IEEE, ISBN:
978-0-7381-9107-2.
IEEE Guide for the Protection of Shunt Capacitor Banks, IEEE Std. C37.992000, May 2000, IEEE, ISBN: 978-0-7381-1979-3.
IEEE Standard for Requirements, Terminology, and Test Code for Dry-Type
Air-Core Series-Connected Reactors, IEEE Std. C57.16-2011, February 2012,
ISBN: 978-0-7381-7143-2.
IEC High-Voltage Switchgear and Controlgear - Part 100: Alternating Current
Circuit-Breakers, IEC 62271-100 ed2.1, 2012, International Electrotechnical
Commission.
M.F. McGranaghan, W.E. Reid, S. Law, D. Gresham, “Overvoltage Protection of
Shunt Capacitor Banks Using MOV Arresters,” IEEE Transactions PAS, Vol.
103, No. 8, pp. 2326-2336, August, 1984.
S. Mikhail, M.F. McGranaghan, “Evaluation of Switching Concerns Associated
with 345kV Shunt Capacitor Applications,” IEEE Transactions PAS, Vol. 106,
No. 4, pp. 221-230, April 1986.
G. Hensley, T. Singh, M. Samotyj, M.F. McGranaghan, R. Zavadil, "Impact of
Utility Switched Capacitors on Customer Systems - Magnification at Low
Voltage Capacitors," IEEE Transactions PWRD, pp. 862-868, April 1992.
G. Hensley, T. Singh, M. Samotyj, M.F. McGranaghan, T.E. Grebe, "Impact of
Utility Switched Capacitors on Customer Systems, Part II - Adjustable Speed
Drive Concerns," IEEE Transactions PWRD, pp. 1623-1628, October 1991.
15
[18]
J. Harder, “AC Filter Arrester Application,” IEEE Transactions on Power
Delivery, Vol. 11, No 1, p. 1355, July 1996.
[20]
van der Sluis, L., Janssen, A. L. J. “Clearing Faults Near Shunt Capacitor Banks.”
IEEE transactions on power delivery 5, no. 3 (July 1990): 1346–1354.
[19]
[21]
J.A. Bonner, W.M. Hurst, R.G. Rocamora, M.R. Sharp, R.F. Dudley, J.A. Twiss,
“Selecting Ratings for Capacitors and Reactors in Applications Involving
Multiple Single-Tuned Filters,” IEEE 94 SM 457-2 PWRD, July 1994.
P. G. Mysore, B. A. Mork, H. J. Bahirat “Improved Application of Surge
Capacitors for TRV Reduction When Clearing Capacitor Bank Faults” IEEE
Transactions PWRD vol. 25 no. 4 pp 2489-2495
16
APPENDIX A
A.1
Overview of Capacitor Bank Switching Transients
Transient voltages and currents are a result of sudden changes within the electric
power system. Opening or closing of a switch or circuit breaker causes a change in
circuit configuration and the associated voltages and currents. A finite amount of
time is required before a new stable operating point is reached. All transients are
caused by either connection or disconnection of elements within the electric circuit
or injection of energy due to a direct or indirect lightning strike or static discharge.
[note: a restrike (or reignition) is reconnection of circuit elements with stored
energy]
A.2
Isolated (Single) Capacitor Bank Switching Transients
Utility capacitor bank switching is a normal system operation and the resulting
transient voltages and currents are usually not a problem for utility equipment.
However, there is a possibility that these relatively low frequency transients can
cause severe secondary transients if a customer has power factor correction
capacitors or result in nuisance tripping of power electronic-based devices, such as
adjustable-speed drives. Power quality problems related to utility capacitor bank
switching include customer equipment damage or failure, nuisance tripping of
adjustable-speed drives or other process equipment, transient voltage surge
suppressor failure, and computer network problems.
Transient overvoltages and overcurrents related to capacitor bank switching are
classified by peak magnitude, frequency, and duration. These parameters are useful
indices for evaluating the effect of these transients on utility and customer
equipment. The absolute peak voltage, which is dependent on the transient
magnitude and the point on the fundamental frequency voltage waveform at which
the event occurs, is important for dielectric breakdown evaluation. Some
equipment and types of insulation, however, may also be sensitive to rates-ofchange in voltage or current.
Energizing a shunt capacitor bank from a predominantly inductive source creates an
oscillatory transient that can approach twice the normal system peak voltage (Vpk).
The characteristic frequency (fs) of this transient is given by the following
expression:
fs =
1
2π L s C
= f system ×
Xc
MVA sc
1
= f system x
= f system x
Xs
Mvar3φ
ΔV
Where:
fs = characteristic frequency (Hz)
Ls = positive sequence source inductance (H)
17
(13)
C = capacitance of bank (F)
fsystem = system frequency (50 or 60 Hz)
Xs = positive sequence source impedance (ohm)
Xc = capacitive reactance of bank (ohm)
MVAsc = three-phase short-circuit capacity (MVA)
Mvar3φ = three-phase capacitor bank rating (Mvar)
∆V = steady-state voltage rise (per-unit)
For example, the characteristic energizing frequency for a 4.8 Mvar, 13.8 kV
distribution capacitor bank with source strength (I3φ) of 10 kA may be
approximated using the following expression:
fs =
1
2π L s C
= f system ×
Xc
MVA sc
1
= f system x
= f system x
Xs
Mvar3φ
ΔV
Where:
MVA sc = 3 x 13.8 kV x 10 kA = 239.02 MVA
(14)
(15)
The steady-state fundamental frequency voltage rise for this case may be
approximated using the following expression:
 Mvar3φ 
4.8 
 x100 = 
ΔV = 
 x100 = 2.0%
 239.02 
 MVA sc 
(16)
Relating the characteristic frequency of the capacitor bank energizing transient (fs)
to a steady-state voltage rise (∆V) design range provides a simple way of quickly
determining the expected frequency range for utility capacitor bank switching. For
example, a 60 Hz system with a design range of 1.0% to 2.5% would correspond to
characteristic frequency range of 380 Hz to 600 Hz. For a shunt capacitor bank on a
utility bus, feeder/cable capacitance and other nearby capacitor banks cause the
energizing transient to have more than one natural frequency. However, for the
first order approximation, this equation can still be used to estimate the dominant
frequency.
Because capacitor voltage cannot change instantaneously, energization of a
capacitor bank results in an immediate drop in system voltage toward zero,
followed by an oscillating transient voltage superimposed on the fundamental
frequency waveform. The peak voltage magnitude depends on the instantaneous
system voltage at the instant of energization and can approach twice the normal
system voltage. For a practical capacitor bank energization without trapped charge,
system losses, loads, and other system capacitances cause the transient magnitude
to be less than the theoretical 2.0 per-unit.
18
Typical magnitude levels range from 1.3 per-unit to 1.8 per-unit and typical
transient frequencies generally fall in the range from 300 Hz to 1000 Hz. [note:
distribution system capacitor energizations tend to produce lower overvoltages
than bus connected transmission voltage capacitors] Figure 6 shows an example of
a measured distribution system capacitor bank energizing transient voltage
waveform that has a peak magnitude of 1.35 per unit and an energizing frequency of
540 Hz.
Figure 6. Example of a distribution
capacitor bank energizing transient voltage waveform.
A.3
Back-to-Back Capacitor Bank Switching Transients
Energizing a shunt capacitor bank with an adjacent capacitor bank already in
service is known as back-to-back switching. High magnitude and high frequency
currents will flow between the capacitor banks when the second capacitor bank is
energized. This current may need to be limited to acceptable levels for switching
devices and current transformer burdens. Often, fixed series reactors (TLIs) are
used with each capacitor bank to limit the current magnitude and frequency. Preinsertion resistors and/or inductors may also be used with some types of switches.
The frequency and magnitude of the inrush current during back-to-back switching
depends upon the rating of the discharging capacitor bank, the impedance of the
19
discharging loop, and the instantaneous capacitor bank terminal voltage at the time
of contact closure.
The impedance of the discharging loop is determined by the inductance between the
capacitor banks, rather than the system inductance. This causes the magnitude of
the inrush current to be much higher than for isolated capacitor bank energization.
Typically, the inrush current lasts for only a fraction a power frequency cycle.
Figure 7 shows an example measured distribution feeder capacitor bank back-toback switching transient current waveform that has a peak magnitude of 602.4
amps and an energizing frequency of 2,040 Hz.
August 02, 1993 at 13:56:33 Local
Max 602.3
Min -602.4
Amps
4095
Phase C Current
Wave Fault
800
600
400
200
0
-200
-400
-600
-800
0
20
40
60
Time (mSeconds)
80
100
Electrotek
Figure 7. Example of a measured feeder current during back-to-back switching.
The high-frequency inrush current may exceed the assumed transient frequency
momentary capability or peak withstand capability of the switching device (e.g.,
IEEE Std. C37.06 and IEEE Std. C37.012) as well as the I2t withstand of the capacitor
fuses. It may also cause false operation of protective relays and excessive secondary
voltages for current transformers in the neutral or phase of grounded-wye capacitor
banks. The back-to-back inrush current must be evaluated with respect to the
transient frequency momentary capability rating of the switch, as well as the I2t
withstand of the capacitor fuses. If either of these ratings is exceeded, possible
solutions to the excessive inrush currents usually involve:
20
•
•
•
•
•
Adding current-limiting reactors (TLIs) to decrease the peak current and
frequency of the oscillatory inrush current
Adding pre-insertion resistors or inductors to the switching device
Adding synchronous closing control to the switching device
Switching the capacitor bank in smaller increments
Selecting component ratings (e.g., circuit breakers, current transformer
burdens, etc.) to withstand the inrush current characteristics
To control the substation ground mat transients due to the high-frequency inrush
currents, where two or more grounded wye capacitor banks are at the same
location, the capacitor bank neutrals may be directly connected, with a single
connection to ground (single point grounding). Peninsular grounding has also been
effective give reference IEEE C37.99, IEEE 1036.
A.4
Transient Outrush Currents during Nearby Faults
The concern for outrush currents exists when a fault occurs close to the capacitor
bank substation and one of the substation circuit breakers must close into the fault
(e.g., during a reclosing operation). The result is that a high-frequency, highmagnitude current may flow through a circuit breaker that may not be rated for that
duty. The current magnitude and frequency must be evaluated with respect to the
circuit breakers’ close and latch rating. Figure 8 shows a simplified system diagram
that can be used for the evaluation of outrush reactor requirements. The primary
consideration for capacitor banks is that there is sufficient impedance to adequately
reduce the outrush current magnitude and (and sometimes frequency) to the
desired levels.
It is important to note that some transient mitigation methods, such as pre-insertion
devices or synchronous closing control, do not reduce outrush currents because
they only operate when a capacitor bank switch is being closed. The full outrush
current occurs when the resistors are bypassed.
Figure 9 shows an example of a simulated high frequency transient outrush current
from a utility transmission capacitor bank into a nearby three-phase fault. The peak
magnitude of the outrush current is approximately 16.7 kA and the frequency is 2.1
kHz.
21
Inductance Between Bank
& Fault – L2
System
Ipk
Fault
Capacitor Bank Self
Inductance – L1
Capacitor
Bank – C1
Vo
Figure 8. System diagram for outrush current evaluation.
Ioutrush-Main-capcase03(NONE)(2005-03-08 15:21:51)
20000
C urrent (A m ps)
10000
0
-10000
-20000
0.090
0.095
0.100
0.105
Time (sec)
ElectrotekConcepts®
0.110
0.115
TOP, The Output Processor®
Figure 9. Example of a simulated capacitor
outrush current during a power system fault.
22
0.120
Circuit breaker inrush current limitations are specified in ANSI Std. C37.06. (3
options available) These inrush limitations are sometimes applied to the outrush
considerations. Since outrush to a close in fault is a rare occurrence, it is expected at
most twice in the life of a breaker, it does not need to be treated quite the same way
as inrush, which may be daily or more frequent. In 2009, C37.06 was revised to
allow outrush current up to the peak current rating of a circuit breaker (2.6 x the
short-circuit rating) for circuit breakers with a Class C1 or C2 capacitance switching
rating. Prior to this, lacking specific guidance, the industry had used the Ipk x f
product (refer to the notes for Tables 1A, 2A, and 3A in ANSI Std. C37.06-2000). In
many cases the Ipk x f product criterion is unnecessarily restrictive, particularly with
non-oil circuit breakers and small capacitor bank ratings. Many installations have
been made with smaller reactors than required to meet the Ipk x f limitation of ANSI
Std. C37.06-2000. Simply limiting the outrush current into a fault to something less
that the peak current capability of the switching devices where there are no oil
circuit breakers involved and the substation grounding can withstand the higher
transient currents, has often been done.
It is interesting to note that this Ipk x f product is independent of capacitor bank
rating. In other words, the required series inductance is dependent only on the peak
voltage when the circuit breaker closes into the fault. For three-phase capacitor
banks, a reasonably conservative estimate of the peak outrush current is:
f=
1
(17)
2π L eq C1
I pk = V0
I pk x f =
C1
L eq
(18)
V0
2pL eq
(19)
Where:
Ipk = peak current, kiloamperes
f = frequency of outrush transient current
V0 = initial voltage on C1
L1 = self-inductance of C1
L2 = inductance between capacitor bank and fault
Leq = L1 + L2
KVAC = Capacitor bank rating, three-phase kVar
C1 = total bank capacitance (microfarrads)
L = Inductance per phase between capacitor bank and fault (microhenries)
23
With parallel capacitor banks, there are a number of different ways to configure the
capacitor banks and required series inductors (TLIs) if required. A few of the
options are shown in Figure 10. Each option has advantages and disadvantages.
Option 1
Option 2
Reactor to Limit Outrush
Reactors Sized for Inrush
and Outrush
Requirements
Smaller Reactors to Limit
Inrush (back-to-back)
Option 3
Reactor to Limit Outrush
Closing Resistors/
Inductors and/or Synch.
Closing Control to Limit
Inrush
Figure 10. Inrush and outrush reactor alternatives.
1)
2)
3)
Option 1: Separate TLIs for inrush and outrush requirements. When a
larger TLI is needed for outrush, a common TLI for limiting outrush
current, in addition to smaller TLIs for inrush current limiting, may be the
optimum configuration.
Option 2: Series TLIs rated for inrush and outrush in series with each
capacitor bank. If the TLI cost is not significantly dependent on its
millihenry rating, then this option may be more economical than Option
1. However, with two equal capacitor banks in parallel, the TLI
millihenry value required to control outrush may be more than double
the single capacitor bank rating.
Option 3: TLI for outrush only, switching device limit inrush. If inrush
current for back-to-back switching can be limited to acceptable levels
without TLIs, this is probably the most economical configuration. Closing
resistors, pre-insertion inductors or a closing control to close the contacts
near voltage zeros are common alternate methods to limit the inrush
current. The single TLI is used to is used to limit outrush currents to
24
acceptable levels. A disadvantage of this option is the high-current
magnitude and frequency that can occur in the event of a restrike on
opening.
For circuit breakers with C1 or C2 capacitor switching ratings, the new limitation in
IEEE C37.09-2009 of keeping the peak outrush current below 2.6 x the short-circuit
current rating of the breaker, effectively eliminates the need for outrush inductors
for many installations based on circuit breaker limitations alone.
Traditionally, when evaluating outrush, closing outrush was investigated. A line
breaker was closed into a fault with a capacitor bank on the source side. This can
result in contact burning and for vacuum breakers, contact welding. A somewhat
different form of outrush can occur on opening.[20] We call it “reignition outrush”.
From the perspective of transmission line circuit breakers during fault interruption,
the presence of one or more capacitor banks represent a large source side
capacitance and also a source of outrush currents. Both source side capacitance and
outrush currents influence the fault interrupting process and may also influence the
fault interruption time. Such a case is illustrated in Figure 11.
L1
SW1
C1
L’
Us
Ls
CB
is
Key
Us
Ls
CB
Source voltage
Short-circuit inductance
Line circuit breaker
L'
L1
SW 1
is
Short-circuit current
C1
Transmission Line
Fault
Busbar inductance
Inductance of damping reactor
Capacitor
bank
switching
device
Capacitor bank
Figure 11. Transmission line circuit breaker
interrupting a fault near a capacitor bank.
25
Transmission line circuit breaker (CB) interrupts a fault (s) on the transmission line.
Assuming that the harmonic distortion is below 5%, the capacitor bank (C1)
modifies the source side TRV to a 1-cos waveshape with a higher peak than the
values given in IEC 62271-100 [2] or IEEE C37.06 [3]. For this phenomenon to
occur the capacitor bank must be at the same voltage level and not connected to the
bus by cable or overhead line.
When a fault occurs on the line, the capacitor bank will discharge into the fault
through the closed circuit breaker (outrush). During interruption, the low du/dt of
the modified TRV waveshape may result in a shorter minimum arcing time than
demonstrated during the type tests. Arcing times shorter than the minimum arcing
time may result in reignition of the circuit breaker and the capacitor bank will
discharge into the fault again (reignition outrush). The contribution of the capacitor
bank depends on the instantaneous voltage at the time of re-ignition and the
inductance (L1 +L') between the capacitor bank and the fault. In the extreme case,
the voltage just prior to breakdown can exceed 2 p.u. That would make the outrush
current 2 times a closing outrush. The large outrush current can have a substantial
frequency (several kHz) and it will create additional current zeros. Depending on
the type of circuit breaker used (e.g. vacuum, oil, air or SF6) it may interrupt at one
of the high frequency current zeros. Such an interruption is associated with
overvoltages. Adding inductance into the circuit will limit the outrush current and
frequency, but may result in an easier switching case for the circuit breaker (i.e. it
may now be able to interrupt in one of the high frequency current zeros) creating
overvoltages. The overvoltages could lead to additional high energy reignitions and
ultimately a failure to interrupt. Any surge arresters on the bus or capacitor side
could experience capacitor bank discharge from reignition outrush and
interruption, from the prospective overvoltage.
Although the events described above are theoretically possible, and have been
demonstrated in power lab tests [20], there is no documented evidence of such an
overvoltage event occurring in actual power system service.
The impact of reignition outrush on a circuit breaker is quite different than a closing
outrush, or normal switching inrush. The contacts are opening, not closing so
contact welding would not be expected to occur, nor would contact wear from
closing contact “chattering”. The di/dt on a reignition outrush could be 2 x that of a
closing outrush which could result in a more severe shock wave for an oil circuit
breaker during a reignition outrush event.
The di/dt capability of bulk oil breakers is believed to be more than two times the
20 kA kHz limit for general purpose oil breakers recommended by standards. This is
based on the difference between a general purpose oil breaker and a “definite
purpose” oil breaker being the presence of high ohmic value opening resistors. On
closing, these resistors only reduce the impact of inrush to about 80%, because they
have a high ohmic value. So from a closing point of view, there is little difference
between a definite purpose oil breaker and a general purpose oil breaker.
26
Historically, the general purpose oil breaker without the opening resistors, was
never tested for capacitive inrush duty.
The likelihood of a reignition outrush occurring depends on the fault parameters,
the circuit breaker performance, and the precise timing of the contact opening
against the current zeros. It is estimated that the likelihood of a reignition outrush of
> 1.0 p.u. occurring is <10% for a close in fault. This is based on an assumption that
only a narrow timing window of about 1 ms will result in a reignition voltage above
1.0 p.u. A close in fault is also a rare occurrence, as are short-circuit currents close to
the breaker rating.
Based on good field performance, and the small likelihood of a severe reignition
outrush occurring, it is recommended that closing outrush continue to be the design
base for outrush analysis. When the peak current rating of the breaker (2.6 x ShortCircuit Rating) is used as the outrush limit, a risk assessment should be made
concerning the likelihood of reignition outrush during clearing of a close in fault. A
reignition outrush could be up to 2 x a closing outrush. If reignition outrush is taken
into account, the design base for the closing outrush analysis should only be ½ of
the breaker’s peak current capability for the outrush limit. (i.e. 1.3 x Short-Circuit
Rating).
A.5 Transient Overvoltages from Capacitor Bank De-Energizing and
Restrikes
When a capacitor bank is de-energized the capacitor will retain a DC trapped charge
equal to the voltage at the time of current interruption. Because the current is close
to 90 degrees out-of-phase to the voltage, at the time of current interruption the
voltage will be at a peak and therefore a trapped charge of near 1.0 per-unit will
remain on the capacitor bank. After current interruption, the system voltage
continues (at 60 Hz or 50 Hz power frequency) on the source side of the switching
device while the DC trapped charge remains on the capacitor bank side of the
device. Because the time constant of the capacitor bank discharge is on the order of
40 s, the DC trapped charge drains very slowly. For a grounded wye capacitor bank,
one half cycle after current interruption (8.33 ms for 60Hz or 10 ms for 50 Hz) the
voltage across the switching device will be near 2.0 p.u. For an ungrounded
capacitor bank, switched with a device where the time difference between poles is
<90 electrical degrees, the recovery voltage will be 2.5 p.u. If a switching device
with >210 electrical degrees between poles is used, the recovery voltage can reach
4.1 p.u. If the dielectric withstand of the contact gap of the switching device has not
had adequate time to recover (or if local stress enhancements have compromised
the dielectric strength) when the 2.0 p.u.( 2.5 p.u. or 4.1 p.u.) is imposed across the
contacts, a dielectric breakdown can occur and current will start to flow again. This
is known as a restrike if the voltage breakdown occurs longer than the first ¼ cycle
following current interruption. A breakdown with < 1.0 p.u. voltage is called a reignition if breakdown occurs during the first ¼ cycle following current interruption.
27
Refer to Figure 12 for an illustration of a single restrike on a grounded capacitor
bank.
Current Through Switching Device
Voltage on Each Side of Switching Device
Peak overvoltage
from 1st restrike
Voltage on system
side of switching
device (60 Hz
system voltage)
First restrike
occurs and
current is reestablished
Current is
interrupted
Voltage on
capacitor bank side
of switching device
(DC trapped charge)
Figure 12. Illustration of a single restrike.
If a restrike occurs near one half cycle following interruption, peak transient
overvoltages more severe than those from normal capacitor bank energizing can
occur because the voltage collapsed across the switching device is near 2.0 p.u.
where for normal capacitor bank energizing it is 1.0 p.u. Theoretically, restrikes can
lead to overvoltages across the capacitor of 3.0 p.u. total for a single restrike. For
some switching devices, if a restrike occurs and the resulting inrush current
following the restrike is interrupted multiple restrikes can occur leading to voltage
escalation and much higher overvoltages. Refer to Figure 13 for an illustration of a
multiple restrike on a grounded capacitor bank. Figure 14 provides another
illustration of a restrike where multiple restrikes occur on successive voltage peaks
(½ cycle intervals) with no voltage escalation.
28
Current Through Switching Device
Voltage on Each Side of Switching Device
Peak overvoltage
from 1st restrike
High frequency
current is
interrupted
Voltage on system
side of switching
device (60 Hz
system voltage)
First restrike
occurs and
current is reestablished
Current is
interrupted
Voltage on
capacitor bank side
of switching device
(DC trapped charge)
Second restrike occurs and
current is re-established
Peak overvoltage
from 2nd restrike
Figure 13. Illustration of multiple restrikes and voltage escalation.
Current Through Switching Device
Voltage on Each Side of Switching Device
Peak overvoltage
from 1st restrike
Successive restrikes occur and
current is re-established
Voltage on system
side of switching
device (60 Hz
system voltage)
First restrike
occurs and
current is reestablished
Peak overvoltages
successive restrikes
Current is
interrupted
Voltage on
capacitor bank side
of switching device
(DC trapped charge)
Second restrike occurs and
current is re-established
Peak overvoltage
from 2nd restrike
Figure 14. Illustration of multiple restrikes with no voltage escalation.
The probability of having a restrike on a switching device is dependent on the
device type and design. Many devices in use today for capacitor switching are
classified as having a low or very low probability for a restrike (Class C1 or C2).
Mitigation techniques such as controlled opening (synchronous-open control) can
29
be used to further reduce the probability of restrikes, and surge arresters are often
applied to protect system equipment in the event that a restrike occurs.
30
APPENDIX B
B.1
Capacitor Bank Switching Transient Mitigation Methods
The devices currently available for transient overvoltage control either attempt to
minimize the transient overvoltage (or overcurrent) at the point of application, or
limit (clip) the overvoltage at local and remote locations. These devices include:
•
•
•
•
Pre-insertion devices (resistors and/or inductors)
Synchronous closing control (also known as zero voltage closing)
Fixed inductors/reactors
Surge arresters (metal oxide varistors – MOVs)
Previous studies (digital simulation and Transient Network Analyzer [TNA]) have
suggested that the effectiveness of these control methods is system dependent, and
that detailed analysis is required to select the optimum transient mitigation scheme.
While often justifiable for large transmission applications, analysis of distribution
system capacitor applications is rarely performed, and in general, capacitor banks
are installed without transient overvoltage control.
Each of these transient control methods has various advantages and disadvantages
in terms of transient overvoltage reduction, cost, installation requirements,
operating/maintenance requirements, and reliability. Some of these techniques
may be useful in controlling the transients when re-energizing a capacitor bank
before the voltage has decayed to near zero.
B.2
Pre-Insertion Devices
A pre-insertion impedance (e.g., resistor or inductor) provides a means for reducing
the transient currents and voltages associated with the energization of a shunt
capacitor bank. The impedance is shorted-out (bypassed – refer to Figure 15)
shortly after the initial transient dissipates, thereby producing a second transient
event. The insertion transient typically lasts for a small fraction of one cycle of the
system frequency. The performance of a pre-insertion impedance is evaluated using
both the insertion and bypass transient magnitudes, as well as the capability to
dissipate the energy associated with the event, and repeat the event on a regular
basis. Pre-insertion resistors and high-loss pre-insertion inductors are one of the
most effective means for controlling capacitor bank energizing transients.
31
Shorting Contact
ts
Phase A
Rp
Lp
tp
Pre-Insertion Contact
.
(repeated for phases B & C)
Figure 15. Illustration of a pre-insertion capacitor bank switch.
The optimum resistor value (Roptimum) for controlling capacitor bank energizing
transients depends primarily on the capacitor bank rating and the source strength.
It should be about equal to the surge impedance (Zs) formed by the capacitor bank
and source impedance and it may be approximated using the following expression:
R optimum =
Ls
C
(20)
Where:
Ls = positive sequence source inductance (H)
C = capacitance of bank (F)
This value results in a slightly underdamped insertion transient. For example, the
optimum resistor rating (Roptimum) for a 4.8 MVar, 13.8 kV distribution capacitor
bank with a source strength (I3φ) of 10 kA may be approximated using the following
expression:
R optimum =
2.11 mH
= 5.62ohms
66.86 μF
(21)
The positive sequence source inductance (Ls) and the capacitance of the bank (C)
may be determined using the following expressions:
kV
Ls =
3
I sc
2π f system
13.8
=
3
10 = 2.11 mH
2π 60
32
(22)
C=
Mvar
4.8
=
= 66.86 μF
2
2πf system x kV
2π 60 x 13.8 2
Where:
(23)
Ls = positive sequence source inductance (H)
C = capacitance of bank (F)
kV = phase-to-phase rms bus voltage (kV)
fsystem = system frequency (50 or 60 Hz)
MVAsc = three-phase short-circuit capacity (MVA)
Isc = three-phase short-circuit current (kA)
Mvar = three-phase capacitor bank rating (MVAr)
Pre-insertion inductors, which were traditionally used primarily for overcurrent
control for back-to-back capacitor switching applications also provide transient
overvoltage magnitude reduction. The degree of overvoltage reduction achieved is
largely determined by the relative size of the source inductance and the resistance
and inductance of the pre-insertion inductor. Pre-insertion inductors are generally
very effective for overvoltage reduction if the inductance is equal to or greater than
the source inductance. Pre-insertion inductors with high resistance further increase
reduction in overvoltages by increased damping of the oscillatory transient portion
of the capacitor-switching voltage transient.
Power ratings for pre-insertion devices need to include the transient inrush and
power frequency currents for the duration of the pre-insertion period. They should
also have some margin for power frequency and harmonics beyond the preinsertion time.
Figure 16 shows an example of a transient simulation for energization of a
substation capacitor bank without and with a pre-insertion resistor. For the studied
system, the maximum energizing transient overvoltage is reduced from 1.77 perunit to 1.29 per-unit with addition of a 6.4 ohm pre-insertion resistor.
33
Capacitor Bank Energizing
1
1
0
Voltage (per-unit)
2
Voltage (per-unit)
2
-1
-1
-2
0.06
Capacitor Bank Energizing - Pre-Insertion Resistor
0
0.07
Electrotek Concepts®
0.08
0.09
Time (sec)
0.10
0.11
-2
0.06
0.12
TOP, The Output Processor®
0.07
0.08
0.09
Time (sec)
0.10
Electrotek Concepts®
0.11
0.12
TOP, The Output Processor®
Figure 16. Illustration of the effect of a
pre-insertion resistor during capacitor bank switching.
B.3
Controlled Closing (Point on Wave Closing Control)
Controlled closing is independent contact closing of each phase near a voltage zero,
as illustrated in Figure 17. To accomplish closing at or near a voltage zero (avoiding
high prestrike voltages); it is necessary to apply a switching device that maintains a
dielectric strength sufficient to withstand system voltages until its contacts touch.
Although this level of precision is difficult to achieve, closing consistency of ±0.5
milliseconds is possible. Previous research has indicated that a closing consistency
of ±1.0 millisecond provides overvoltage control comparable to properly rated preinsertion resistors.
The success of a synchronous closing scheme is often determined by the ability to
repeat the process under various (e.g., system and climate) conditions. Adaptive,
microprocessor-based control schemes that have the ability to learn from previous
events address this concern. The primary benefits of this capability are the control’s
ability to compensate for temperature induced differences in making time, (and in
some cases, idle time). This can result in increased reliability (less maintenance) .
Fully discharged grounded capacitor banks are controlled by closing the three
phases at three successive phase-to-ground voltage zeros (60° separation). Fully
discharged ungrounded banks are controlled by closing the first two phases at a
phase-to-phase voltage zero and then delaying the third phase 90 degrees (phaseto-ground voltage zero).
Figure 18 shows an example of a transient simulation for energization of a
substation capacitor bank without and with synchronous closing control. For the
studied system, the maximum energizing transient overvoltage is reduced from 1.54
per unit to 1.11 per unit with a +1.0 millisecond closing error.
34
Ungrounded wye
tab
<delay>
tc= tab + 4.17msec
A
C
B
X
X
X
X
Measured Phase A Voltage Zero
<switch operating time>
ta
tb= ta + 2.78msec
tc= ta + 5.56msec
Grounded wye
60° = 2.78msec
Figure 17. Concept of controlled closing.
Capacitor Bank Energizing
1
1
0
Voltage (per-unit)
2
Voltage (per-unit)
2
-1
-1
-2
0.04
Capacitor Bank Energizing - +1.0msec Error
0
0.05
0.06
0.07
Time (sec)
Electrotek Concepts®
0.08
0.09
-2
0.04
0.10
TOP, The Output Processor®
0.05
0.06
0.07
Time (sec)
Electrotek Concepts®
0.08
0.09
0.10
TOP, The Output Processor®
Figure 18. Illustration of the effect of
controlled closing during capacitor bank switching.
B.4
Surge Arresters
B.4.1 Uses
Surge arresters (e.g., metal oxide varistors [MOVs]) can limit transient voltages to
the arrester's protective level (maximum switching surge protective level, typically
1.8 - 2.5 per-unit) at the point of application. The primary concern associated with
35
surge arrester application is the energy duty during a capacitor bank switch
restrike. Although a rare occurrence, a switch restrike generally results in the
highest arrester duty for arresters located near the switched capacitor bank. In
addition, remote arresters (including low voltage customer applications) may be
subjected to severe energy duties if voltage magnification occurs.
The energy duty requirements for arresters near capacitor bank locations depend
on the ratings of the capacitor bank(s) and arresters. In general, the most severe
duty during a switching event for an arrester near a capacitor bank occurs during a
capacitor bank switch restrike. This is due to the trapped charge on the capacitor
bank at the instant the restrike occurs, resulting in a greater magnitude of the
transient voltage oscillation. Figure 19 illustrates the voltage and current
waveforms for a single capacitor bank switch restrike.
3.00
2.00
Capacitor Current
(before opening)
Restrike occurs
Bus Voltage
Voltage (pu)
1.00
0.00
-1.00
Capacitor Voltage (trapped charge after opening)
-2.00
-3.00
Current is interrupted
Opening signal (contacts begin to part)
16.7
33.3
50.0
66.7
Time (sec)
Figure 19. Illustration of a single capacitor bank switch restrike.
Arresters across a TLI can allow a reduced insulation level to be used for the TLI.
When transient limiting inductors are installed in the neutral of capacitor banks
surge arresters can be applied across the inductor for protection of the inductor and
capacitor bank neutral under switching and lightning events. When this is done
studies should be performed to determine proper coordination between the
arresters protective level and the anticipated overvoltages across the arrester. It
should be verified that under switching events such as capacitor bank energizing
(inrush currents) and re-closing into a close-in fault (outrush currents) the surge
arresters do not short-out the inductor resulting in excessive inrush/outrush
currents.
36
B.4.2 Drawbacks
The primary drawback of adding surge arresters is the addition of a potential point
of failure. When a surge arrester fails, the usual failure mode is a short-circuit which
could result in a line-to-ground fault in the substation which could in turn lead to
other potential problems for adjacent equipment such as failure to interrupt the
fault current.
B.4.3 Where in the Circuit to Locate the Surge Arresters
Surge arresters can be located in the following positions as shown in Figure 20:
•
•
•
•
Bus side of the capacitor switching device
Bus side of the TLI
Capacitor side of the TLI
Across the TLI
Switching Transient limiting
Device
inductor (TLI)
Switching Transient limiting
Device
inductor (TLI)
Capacitor
bank
Surge
Arrester
Example with arrester
on bus side of switching device
Example with arrester
on bus side of TLI
Switching Transient limiting
Device
inductor (TLI)
Surge
Arrester
Capacitor
bank
Surge
Arrester
Switching Transient limiting
Device
inductor (TLI)
Capacitor
bank
Surge
Arrester
Example with arrester
on capacitor side of TLI
Capacitor
bank
Example with arrester across TLI
Figure B.6 – Example locations for surge arrester placement.
Each of the locations above have been successfully used when proper insulation
coordination studies have been performed for the substation, but each potential
location has its own advantages and disadvantages. The table below shows a
comparison of some potential advantages and disadvantages for each location.
37
Location of
Arrester
Bus Side of
Switching Device
Bus Side of TLI
Capacitor Side
of TLI
Across TLI
Advantages
Disadvantages
- Provides protection for
switching device from
lightning/switching surges when
open
- Provides protection for TLI
from fast front surges (e.g.,
lightning)
- Provides less protection for
the capacitor bank because of
voltage rise across TLI
- Provides protection for TLI
from fast front surges
- Provides less protection for
the capacitor bank because of
voltage rise across TLI
- Provides best protection for
the capacitors
- Provides less protection for
the TLI from fast fronted surges
(e.g., lightning)
- If surge arrester fails to ground,
high rate-of-rise TRV's can be
imposed on the breakers
- Provides protection for the
TLI from lightning/switching
surges
- Can reduce TRVs from reactorlimited faults
- Arrester does not see full lineto-ground voltage during normal
operation
- Does not protect the
capacitor bank from
lightning/switching surges
- Failure of arrester would shortout the TLI
B.4.4 How to Size the Surge Arresters
The size and location of the surge arresters should be determined in an insulation
coordination study for the substation considering the desired insulation levels,
location, and rating of surge arresters. Furthermore, the potential energy dissipated
by the arrester should be calculated in the event of a restrike during capacitor bank
de-energization. IEEE Std C62.22-2009 “IEEE Guide for the Application of MetalOxide Surge Arresters for Alternating-Current Systems” provides guidance for
selecting surge arresters to protect the substation equipment including shunt
capacitor banks.
38
APPENDIX C
Example 230kV Capacitor Bank TLI Study
C.1
Terminology
The inductor placed in series with an isolated (single) capacitor bank is usually
installed to control the magnitude of outrush current from the capacitor bank to a
breaker closing into a fault. Often, as in the case of this 230kV example, this is a line
breaker closing into a close in fault on its terminals.
These inductors are referred to as:
•
•
•
C.2
“Damping Reactors” this is IEC terminology
“Current Limiting Reactors (CLRs)” common usage in the USA, but also
applies to larger inductors used to limit fault current magnitudes.
“Transient Limiting Inductors” (TLI) this is the Capacitor Subcommittee’s
choice since the terminology “reactor” is somewhat archaic.
Introduction
What problem is trying to be solved in using a TLI?
Capacitor bank discharge current “Outrush” through a closed breaker is not harmful
to the breaker unless the current exceeds the peak current capability of the breaker
(2.6 x short-circuit rating).
Technically, the Capacitor discharge current will add to the 60 Hz short-circuit
current. However, because the outrush current frequency is typically 30x or more
than 60 Hz, and the capacitive outrush damps out in a few milliseconds, the 60Hz
fault current component will only add a few percent to the peak current, and for
purposes of simplicity will be ignored.
IEEE Standard C37.06-2009 clause 7.4 note (8) [found on page 32] states:
“(8) For Class C1 and C2 circuit breakers exposed to transient inrush currents from
nearby capacitor banks during fault conditions, the capacitance transient inrush
peak current shall not exceed the close and latch (peak withstand) capability of the
circuit breaker. This is considered an infrequent event, and therefore the circuit
breaker should be expected to handle this duty twice in its life time without
requiring maintenance of the contacts.”
Thus for SF6 breakers the breaker limitation on outrush through a closing breaker is
the same as for a closed breaker: The peak current magnitude must not exceed 2.6 x
the short-circuit rating of the breaker. There is no limitation on frequency of the
outrush current.
39
C.3
Equations for Calculating the Outrush Current
When the Example 230 kV Capacitor is installed, all of the 230 kV Circuit breakers
will be SF6 puffer type with no arc assist, and with a 63 kA short-circuit rating. All
are class C1 capable. Note (8) under clause 7.4 of IEEE C37.06-2009 [found on page
32] applies. Therefore, the peak outrush current must be limited to 2.6 x 63 =
163.8kA. While it is true that the Capacitive discharge will be added to the 60Hz
fault current, the outrush current usually has a frequency in the range of 30 (or
more) x 60 Hz and damps quickly. Thus the outrush current is mostly over before
the 60 Hz fault current amounts to much. For simplicity, we will ignore the 60 Hz
component.
The outrush current can be modeled as a series RLC circuit. The example capacitor
is a grounded wye so we can look at one phase.
The C is provided by the capacitor bank.
C=
Var
ωV 2
(24)
Where:
C = capacitance in microfarads
V = rms kV
ω = 377 (for 60Hz)
Note: If Var is three-phase, V is line to line kV
If Var is single phase, V is line to ground kV
To calculate the outrush current, one needs the capacitance of the bank as well as
the total inductance (L) of the series circuit. The inductance (L) is the sum of bus
work inductance, connections inductance (including the neutral connections, the
capacitor bank self inductance, and any added discrete inductance (the TLI when
applicable).
•
•
•
For typical 230 kV bus and connections, assume 0.3 µH/foot.
For a 230 kV cap bank assume 10 µH for the bank itself.
[If you want to get fancy you can calculate the bank inductance. A
capacitor unit is 1.0 µH, String/wiring is 0.4µH/ft.]
Since the circuit is under-damped, for conservatism, we will ignore the resistance
when calculating the peak current and frequency. (The resistance will lower the
peak and depress the frequency slightly)
I peak = Vpeak x C
L
40
(25)
Where:
C = capacitance in Farads
L = the inductance in Henries
Vpeak = the crest of the voltage which can be calculated as follows:
Vpeak = VL−L_RMS x 2
3
The frequency of the outrush current can be calculated as follows:
f=
1
2π LC
C.4
(26)
(27)
Outrush Current Calculation for Example Capacitor Bank
Assume the fault is at the line side bushings of a line breaker since that will give the
highest peak current because it will have the lowest inductance. The circuit distance
is 60’ + 52’ (bay width) +50’ to the capacitor bank for a length of 162’ corresponding
to the following inductance:
L = 0.3µH / ftx162 ft + 10 µH = 58.6 µH
For the initial bank, the rating = 82 Mvar at 230 kV
Cinitial
82 x10 6
=
= 4.1µF
377 x 230 2
The maximum (future) bank rating 205 Mvar at 230 kV
C µax
204 x10 6
=
= 10.3µF
377 x 230 2
(28)
(29)
(30)
Therefore, the outrush current peak and frequency for the initial and maximum
rated capacitor bank sizes are as follows:
I initial = 230 x 2 x 4.1
= 49.7kA
3
58.6
f initial =
1
2π 58.6 x10 −6 x 4.1x10 −6
= 10kHz
= 78.7kA
I max = 230 x 2 x 10.3
3
58.6
41
(31)
(32)
(33)
f max =
1
2π 58.6x10 −6 x10.3x10 −6
= 6.5kHz
Since 78.7 kA < 163.8 kA, no TLI is required.
(34)
Even allowing for a reignition outrush 78.7 kA< 81.9 kA (163.8/2)
One needs to remember that although there will not be damage to the circuit
breaker from outrush, there are possible protection and control system concerns.
The outrush current will generate transient ground rise between the capacitor bank
and the point of fault. While the chosen fault location produces the largest outrush
current, which is important for the circuit breakers, another location, perhaps on
the other side of the control cubicle could produce worse control system transients.
Current circuits are normally grounded in the control cubicle. This remote ground
is present on the CT cores and on the CT terminal blocks at the line breakers.
During an outrush event, there will be a significant potential difference (many kV)
between the CT star point at the circuit breaker, and the Control cubicle ground.
Placing a 20mm diameter 1000 V MOV from the CT star point to local ground will
safely clamp that potential difference. If high impedance relays are used for bus
differential, then MOVs (1000 V 20 mm diameter) should be placed across the CT
windings. [MOV voltage ratings can be determined using the standard insulation
coordination procedures. The voltage rating is straight forward. Energy calculations
are quite complex. The above ratings have been used successfully for more than 20
years.] All CT secondaries on the capacitor bank should be protected with MOVs on
their terminals.
Also the high di/dt from an outrush will produce common mode voltages on any
unshielded control or power cables near the outrush, or outrush return, path.
Oil breakers have limits on closing, when initiating a capacitive discharge, both on
the peak current and the frequency. Vacuum and SF6 breakers have limits on
closing outrush current magnitude. Details of this limitation will be discussed in the
Appendix D “Capacitor Bank TLI Sizing and Application Guide Including TRV
Mitigation”.
42
APPENDIX D
Capacitor Bank TLI Sizing and Application Guide Including TRV Mitigation
D.1
Terminology
The inductor placed in series with an isolated (single) capacitor bank is usually
installed to control the magnitude of outrush current from the capacitor bank to a
breaker closing into a fault. Often, as in the case of the example in Appendix C, this
is a line breaker closing into a close in fault on its terminals. These inductors are
referred to as “Transient Limiting Inductors (TLI)” This is the Capacitor
Subcommittee’s choice.
“Transient Recovery Voltage (TRV)” this is the circuit response to a current
interruption at a naturally occurring current zero.
“Initial Transient Recovery Voltage (ITRV)” is the fast traveling wave
component of TRV at a Bus see IEEE C37.04 1999 clause 5.9.2.3
“Short Line Fault (SLF) TRV” is sawtooth traveling wave TRV which results
from a fault on a roughly 1km line length. It is defined in terms of percentage
of the terminal fault current rating as decreased by a short line segment. See
IEEE C37.04-1999 5.9.2.2
“Fast TRV” is a 1-cosine wave shape TRV from an inductor or Transformer limited
fault. See IEEE C37.06.1-2000 where a fast TRV is demonstrated by a special test
which has a maximum steepness about 5 times the “normal” 30% terminal fault
requirement.
Information needed to conduct study:
•
•
•
•
Short-circuit duty to be used. i.e., actual short-circuit levels now and future,
or design base short-circuit level.
Voltage rating
Initial and ultimate capacitor bank size, Mvar
Circuit breaker ratings/capabilities of line, tie, transformer breakers in the
station
‒ Interruption technology (SF6 , vacuum, oil, air blast )
‒ Terminal fault rating, if used for breaker failure of capacitor
protection breaker
‒ SLF capability with no added OR INTERNAL capacitance (90%SLF)
‒ ITRV capability with no added or internal capacitance
‒ Does breaker pass Fast TRV requirements of C37.06.1-2007?
•
Capacitor protection breaker ratings/capabilities
‒ Terminal fault rating
‒ SLF capability with no added OR INTERNAL capacitance (90%SLF)
43
•
•
•
•
•
•
D.2
‒ ITRV capability with no added or internal capacitance
‒ Does breaker pass Fast TRV requirements of C37.06.1-2007?
Station Layout
Is there a desire to make the cap bank a harmonic filter?
How transient hardened is the protection/control system?
Is it better to transient harden the control /protection system (i.e install
MOVs where needed) or reduce the severity (di/dt) of outrush and back to
back transients?
Risk aversion to rare fault events as outrush, and total cap bank fault.
For back to back cases, how often will the capacitors be switched back to
back?
‒ What contact life is desired?
‒ What is the back to back wear limit ( cumulative I x t) for the capacitor
switching device?
Introduction
In the Case in Appendix C (230 kV Capacitor Bank), it was found that outrush
limiting TLIs (damping reactors) are not required to protect the Circuit Breakers. If
Vacuum Breakers or Oil breakers were on the bus, the situation would have been
different.
Switchgear Concerns on capacitor switching:
•
•
•
Frequent switching. Capacitors are often switched daily A typical
transmission breaker may switch a few times per year and interrupt shortcircuits a few times per year. Capacitor switching devices, in general, see
several orders of magnitude more operations in its life than line breakers.
Typical expectation is 10,000 operations in a 40 year life for capacitor
switching, compared to 200 operations in the same 40 year life for a line,
transformer, or bus section breaker.
Inrush currents during switching, particularly back to back switching. This is
a frequent event perhaps 10,000 operations in 40 years. Back to back
switching can be particularly onerous. Back to back inrush frequencies range
from 2 – 20 kHz depending on the specifics. The multi-kHz transient arc
tends to be more compact than a 60 Hz arc. The burning on the contacts is
more localized, and can make for dielectric stress enhancements when the
contacts are open. It has been observed that for pin and tulip style contacts,
contact erosion tends to make the pin contact conical. The cumulative I x t
during the time of the closing arc will determine the degree of contact
erosion. Keeping inrush current cumulative I x t below manufacturer’s
recommendations will promote long contact life.
Outrush current when closing into a fault has a higher magnitude and a
similar frequency as back to back inrush currents. The big difference is that
outrush from closing into a fault is expected to be a rare event, occurring only
44
a few times (if ever) in a circuit breaker’s 40 year life. Outrush can possibly
affect all line, transformer, and tie breakers in a station. It does not affect the
capacitor switching breaker (or switch).
Capacitor switching inrush currents can be controlled with: Controlled Switching;
Pre-insertion resistors, and pre-insertion inductors. Fixed TLIs (damping reactors
or CLRs) can also be used to limit inrush transient currents, but are less effective
than controlled switching or properly sized pre – insertion impedances .
Outrush is another matter. Controlled switching is not reasonable to apply to an
infrequently operated line breaker. Closing resistors either are not available on
some breakers, or not sized properly to control outrush. The only practical control
of outrush current magnitudes is with TLIs (Damping Reactors). Tuning Inductors
for a harmonic filter will also be effective in limiting outrush currents.
For SF6 breakers, the inherent self inductance of buswork and leads will usually be
enough to keep outrush currents within their capabilities, since they can withstand
quite large outrush currents without damage.
Vacuum breakers may suffer from serious contact welding if the outrush current is
too high. Serious welding in its most severe form will prevent opening of the
contacts by the driving mechanism. At lower currents, welds breakable by the
driving mechanism may produce stress enhancements on the contacts, or result in
particles sloughing off, either of these can lead to restriking on subsequent
operations. This may be unacceptable for capacitor, unloaded line, or cable
switching. In other applications, restrikes may be less of a concern. Often,
numerous live switching operations will burn off the offending stress enhancement,
or vaporize the free particles.
Oil Circuit Breakers can suffer shock wave damage to the interrupter if the product
of the peak current and the frequency is too high (I x f is too large). The result is
destruction of the interrupting chamber and loss of fault interrupting capability.
D.3 Proposed method for determining Capacitive Inrush (outrush)
capability of circuit breakers
In no case should the Inrush/outrush current exceed 2.6 x the rms short-circuit
rating of the breaker (i.e. close and latch peak current).
For the shock wave portion, based on the prestrike arc shock wave theory:
Ixf = k
(35)
Where:
I = allowable peak current (expressed in same units as short-circuit rating)
f = the natural frequency of the circuit (kHz)
45
k = a constant different for each major interruption technology (and different
for each interrupter design)
For bulk oil breakers: k=85 kAkHz
For SF6 breakers: k= 2500 kAkHz
For Vacuum breakers wishing to attain Class C2 I<7kA regardless of frequency
For Vacuum breakers wishing to attain class C1 I< 20kA regardless of frequency
Based on these proposed limits, the minimum inductance (L) required would be
calculated as follows:
L=
Vpeak
(36)
2pk
One can see that the required minimum L is independent of C. It should be
understood that there is some minimum threshold energy, below which shock wave
damage will not occur. While we don’t know precisely what this energy is,
experience has shown that capacitance in the few nF range does not seem to provide
enough energy to cause shock wave damage.
Equation (36) is only concerned with the shock wave portion of the discharge
energy, much of the energy available from the capacitive circuit is dissipated in the
circuit resistance ( buswork leads and the series resistance of the capacitor bank
itself). Another small portion goes into contact ablation (erosion of the breaker
contacts). It is this portion that may be the limiting feature for SF6 breakers
switching back to back capacitors. Each breaker design will have a limit on the
accumulated I x t during the time that a closing arc is burning during back to back
switching that will give acceptable contact life and switching performance. The
manufacturer should be consulted to tell what this limit is.
For outrush, parametric analysis for SF6 breakers, leads to the conclusion that only a
few 10s of microhenries will be required in most cases, since SF6 is not very
sensitive to shock waves. That minimum inductance will usually be satisfied by the
natural bank and bus inductance.
D.4
Vacuum Breaker Example
Vacuum Breakers as of 2011 are available at voltage ratings up to 145 kV in a single
interrupter.
Let’s assume we want to keep the peak current below 20 kA on an outrush current
and we don’t care about the frequency.
We have:
46
I peak = Vpeak x C
and
C=
L
= 0.816xVL−L x C
L
Var
ωV 2
(37)
(38)
Where:
C = capacitance in microfarads
V = rms kV
L = inductance in micro henries
Note: If Var is three-phase, V is line to line kV
If Var is single phase, V is line to ground kV
Combining and using VL-L:
I peak = 0.816xVL−L x Var
(39)
ωV 2 L
Solving for L:
L=
0.6659xVar
Var
=
0.001766x
2
2
ω x I peak
I peak
(40)
Notice how this inductance value is independent of Voltage, and only depends on
the capacitor Mvar rating.
To keep Ipeak below 20 kA with 28.8 Mvar capacitor bank, an L of 128 µH or greater
is required. To keep Ipeak below 7 kA a larger inductor would be required by a factor
of (20/7)2, giving a required inductance of 1.05 mH.
TRV mitigation for a capacitor bank short will not be considered in this example. If
the capacitor protection breaker is SF6, the methodology is the same as for the 630
µH example under “Line Oil Breaker Example” below. The capacitor will have a
slightly different capacitance. If the capacitor protection breaker is a vacuum
breaker, the fast TRV will be easy for it, and no TRV mitigation may be required.
D.5
Line Oil Breaker Example and TRV Calculations
Let’s assume we had a 50 kA oil breaker that you wanted to protect from outrush
damage.
47
Assume it was determined that the minimum L = 688 µH and there is 58 µH of
natural buswork inductance, so the additional inductance required is 688-58 = 630
µH.
Current ratings for the TLI
Continuous Current:
The minimum continuous current rating should be 1.4 x the maximum continuous
60 Hz current of the capacitor bank calculated as follows for a 230 kV 205 Mvar
capacitor bank:
I continuous
Var
205x10 6
= 1.4x
= 1.4x
= 720A (rounded to 800A) (41)
3xV
3x230x10 3
Short-Circuit Rating:
For a small inductance inductor, the peak current short-circuit rating must equal or
exceed the maximum expected peak current short-circuit duty at the substation.
Usually a minimum of a 1.25 safety factor is applied.
Potential TRV Concern
SF6 breakers have a characteristic low capability to withstand Fast/Steep Transient
Recovery Voltages. This includes short line fault and inductive faults. If a fixed
inductor is more than 1% of the fault impedance, an SF6 breaker may have trouble
with it. The first few microseconds of TRV are very difficult for an SF6 breaker to
withstand. Oil and Vacuum breakers do not have this characteristic.
The TLI is placed in series with the capacitor bank, to limit the outrush current. If a
fault develops shorting out the Capacitor bank, the TLI may comprise more than 1%
of the fault impedance and may cause the breaker TRV trouble. This is true whether
the TLI is placed at the line end or neutral end of the capacitor. An analysis needs to
be done to check if the TLI can cause an excessive TRV for SF6 circuit breakers.
In this example, the short-circuit current is 19.4 kA three-phase and 15.7 kA phase
to ground.
The worst case is generally the greater short-circuit current, but it is unlikely to
have a three-phase short of each capacitor phase simultaneously for this example.
However, we will calculate phase to ground equivalent inductances for both the
single line to ground and three-phase fault currents for this example.
L sourceG
V
230x10 3
=
=
= 22.4 mH
3xIxω
3x15.7x10 3 x377
48
(42)
L source3
V
230x10 3
=
=
= 18.2 mH
3xIxω
3x19.4x10 3 x377
(43)
The next step is to calculate what proportion of voltage will remain on the TLI
during a capacitor fault.
For a good (low loss) inductor, the TRV peak will be 1.8 x the peak voltage during
the fault. (damping factor =0.81) the TRV voltage is a 1-cosine and will start at zero,
and ½ cycle of TRV frequency later, be at the first peak voltage.
For 230 kV use 245 kV x .816 = 200 kVpeak.
For the single phase fault:
L TLI
630x10 −6
x200x1.8 = 10 kV (44)
V=
xVpeak x1.8 =
630x10 −6 + 22.4x10 −3
L TLI + L sourceG
For the three-phase fault:
V=
L TLI
630x10 −6
xVpeak x1.8 =
x200x1.8 = 12 kV (45)
L TLI + L source3
630x10 −6 + 18.2x10 −3
The natural frequency of an air core TLI coil and the connections will be about 700
kHz (from experience) which means the first peak of the TRV occurring in ½ cycle
will be in 0.7 µs.
What is the breaker TRV Capability for this condition?
The ITRV capability is 4.25 kV in 0.6 µs. (not high enough). The SLF capability based
on 90% SLF at 45 kA and no added capacitance is 10.8kV/µs after a 0.5 µs delay. In
this example the breakers are stressed to less than ½ of their no capacitance SLF
capability, and they are “pure” puffers, they may withstand these onerous TRVs,
especially in the single line to ground case. Note: this method is not applicable to
self blast or arc assist interrupters.
So, you may get away with no TRV mitigation. However, without test data, this is a
poorly defendable position.
Determine size of TRV Mitigation Capacitor
Determine target TRV Frequency
Since a 630 µH inductor will have a relatively small proportion of fault voltage
across it, the 90% SLF TRV capability can be used. A 0.5 µs time delay roughly
equates to 30 degrees after the trough of a TRV sine wave. Consider a trapezoidal
wave stating at zero, then after 0.5 µs begins a 10.8 kV/µs rise for 2 µs, then is
49
constant for 1 µs, then heads back down to zero. Thus the period of the wave would
be 360/30 (12) x 0.5 µs = 6 µs. The SLF equivalent TRV frequency is thus 166 kHz.
Where does the 10.8 kV/µs come from? The short line fault TRV is a ramp. The
slope of the current is the di/dt of 60Hz at zero (where the current is extinguished).
The voltage is simply this slope x the assumed surge impedance of 450 ohms. The
unassisted 90% SLF TRV capability is 50 kA. That means the actual current is 90%
of 50 kA = 45 kA so the TRV slope is √2 x 45 kA x 377/s x 450 ohm = 10.8 x 106
kV/second =10.8kV/µs
The equivalent peak to peak amplitude converting a trapezoidal wave to a sine wave
will be 2 µs x 10.8 kV/µs x 2/√3 = 24.8 kV. Our TLI peak to peak voltage is 12 kV.
The 90% SLF TRV first peak = 200 kV x 1.6 x (1-0.9) = 32 kV so we are OK on peak
TRV capability (32 kV>12 kV). Therefore the peak voltage is not a concern. Since
our amplitude is decreased by a factor of 12 /24.8= 0.5. The target frequency can be
increased by √(1/0.5) = 1.4 So our target TRV frequency is 1.4 x 166 kHz = 232
kHz.
What capacitance in parallel with 630 µH will give a frequency of 232 kHz? The
following shows the calculation of the minimum required capacitance:
C=
1
(46)
(2πf )2 L
Where:
f in MHz
C in µF
L in µH
Inserting values for this example:
C=
1
(2p × 0.23)2 630
= 747 pF
(47)
It doesn’t hurt to go larger on the capacitance. For example, a 3750 pF 230kV
capacitor (which is a reasonable size for a 230 kV CCVT) would work for this
example.
Insulation Level
How do we choose the voltage rating? Both of these devices will only see significant
voltage during a capacitor outrush and other high frequency transients such as
lightning. On fast transients, the TLI would be expected to flash over before failing
turn to turn. It basically needs to support voltage across itself during the outrush
condition. It only requires a BIL of about 2.2 x Peak phase to ground voltage, or for a
50
230 kV application, 450 kV. In specifying the TLI insulation level mention that it is
expected to flash over externally before failing turn to turn, for a 1.2 x 50 µs Impulse
(standard BIL waveform). The TRV shaping capacitor, in effect, could be protected
by the coil flashing over, but this is not a truly coordinated system, we don’t know
what the coil flashover will be. The 230 kV system has no line entrance arresters
however there will be nodal reflections of external lightning transients coming in on
a line. With one line out of service, and 1 line coming into 2, the voltage would be
2/3 of the incoming transient voltage. Or 2/3 x 1300 kV = 858 kV. For this
application, it is recommended that the TRV shaping capacitor have a BIL at least to
the 900 kV BIL station insulation. In a case with many 230 kV lines, the insulation
level could be lower.
So:
•
•
TLI BIL minimum 450 kV [an Arrester across the TLI may be advisable to
protect for lightning transients.]
TRV shaping capacitor BIL minimum 900 kV
The foregoing is based on the maximum Capacitor bank size.
Analyze based on the numbers above k = 85 V= 200kV (Using equation 36)
L=
Vpeak
2pk
 Vl − g 
L=
 = (200/533.8) = 375 μH
 6.28x85 
(48)
(49)
From the example capacitor, the inductance to the fault is about 58 µH so the
additional inductance required is 375-58 = 317 µH.
The short-circuit and mechanical peak current ratings are the same as for the 630
µH inductor.
TRV Concern with Smaller inductor.
The first peak of fast TRV will be reduced by a factor of 317/630 = 0.5 since this
approach is less conservative, we will use the line to ground fault inductance. The
first peak will be .5 x 10 = 5 kV. This is still more than the ITRV peak, so that
capability cannot be used. We are stuck with the unassisted 90% SLF TRV. If we
assume that the self capacitance of the inductor and leads is the same as the 630 µH
inductor, the frequency will go up as √(630/317) = 1.4. The assumed frequency of
the 630 µH inductor was 700 kHz, the 317 µH inductor will give a TRV frequency of
1.4 x 700 = 980 kHz. Using the same analysis as above to attain the target natural
51
frequency of the TLI in parallel with a TRV shaping capacitor, we get Target f =
√(28.4/5) x 166 kHz = 395 kHz.
As above:
C=
1
(2pf )
2
L
=
1
(2p × .395)2 317
= 504 pF
(50)
This is smaller than for the 630 µH inductor. The voltage rating concerns are
identical and thus unchanged.
However, as discussed above, the SLF TRV capability is based on a 45 kA fault and
here we have just about 1/3 of that. The SLF TRV capability of a pure puffer (no arc
assist) will undoubtedly be higher. It might be high enough that no parallel
capacitor is required. One could assume that the 0.5 µs SLF TRV delay at 45 kA
could easily drop to 0.15 µs at 16 kA, and the TRV steepness could be much higher.
In My judgment the likelihood of “getting by” with no TRV shaping capacitor is about
85 - 15 in this case.
On a risk basis, the likelihood of a fault of the entire capacitor bank is small, so that
one might just take the risk. However, NERC is aware of this phenomenon after a
TRV failure to interrupt after a Hydro One 230 kV Capacitor bank phase to phase
fault, and issued an alert to all utilities. If such a failure occurred, one would be
“without excuse” at the NERC hearings, and the utility could be fined. The
seriousness would depend on the system consequences.
Harmonic Filter
The above treatment arrived at the minimum inductor size for the TLI (damping
reactor) to protect circuit breakers from outrush damage. There are reasons other
than switchgear limitations, why a larger Inductor might be used.
My thinking in these situations was: “If I have to install an inductor and TRV
mitigation capacitor, it may as well do something useful”.
•
•
•
A larger inductor will reduce the di/dt of the outrush, which would lower
transient ground rise, and lower the induced voltages on control cables.
It would also lower the frequency and amplitude of the normal energizing
transient currents. Whether the change in frequency is a good or bad thing
depends on the details of any downstream voltage magnification issues.
There is some 5th, 7th, 11th, and 13 th harmonic in the system voltage that
could be shunted with a harmonic filter. One can easily tune the Capacitor to
become a harmonic filter branch. Choosing the tuning frequency should be
done with a harmonic study, so the most offending harmonic can be filtered.
Future increase of the capacitor bank size will lower the tuning frequency,
unless new inductors are purchased at that time. Lower order harmonic
52
filters will increase the voltage rating needs of the capacitor bank. The
guidance in IEEE 1531 [3] should be followed.
Reducing Outrush di/dt
If one wished to reduce the outrush di/dt to protect the control system, what would
be a reasonable value?
How about the 60 Hz design short-circuit di/dt? An example for a 63 kA shortcircuit current is shown below:
di
= 2 x 63kA x 2π x 60Hz = 33553kA/s = 3.36x10 7 A/s
dt
If we look at our series RLC formulas and forget the R:
I=V C , ω= 1
, and di = ωI
dt
L
LC
di
dt
= ωI = 3.36x10 7 = 1
Solving for L:
L=
Vpeak
3.36x10
7
= 200x10
LC
xVpeak C
3
3.36x10 7
What is the natural frequency?
f =
L
(52)
(53)
= 5.9 mH (rounded to 6 mH) (54)
1
1
=
= 1 kHz
−3
−6
2π LC 2π 6x10 x4.1x10
That is too high to catch any of the prevalent harmonics.
Harmonic. If we were to target 11th harmonic:
11th (future 7) Harmonic filter
(51)
(55)
1000/60 = 16.7th
L= (16.7/11)2 x 6 mH = 13.8 mH. Actually one would detune to the low side a little
(say 3%) so the inductance would be increased by (1.03)2 to 14.6 mH
For example, let’s choose 14.5 mH. Now we no longer have a TLI (Damping reactor)
but a Filter Inductor.
Continuous current is the same as the TLI or 800 A. If you keep the 14.5 mH
inductor and max–out the bank to 204 Mvar, the natural frequency drops by
√(82/204) 0.63 and voila! You have a 7th harmonic filter!
53
The short-circuit current rating can be a little less because the inductor will
significantly reduce the short-circuit current. In fact, the reduction is the same as
the per unit voltage across the coil during a short-circuit, i.e., 40% reduction (see
below). So the rated short-circuit can be 15 kA for the 14.5 mH inductor.
The mechanical peak is still 2.82 x short-circuit = 42.3 kA
Check TRV Concerns
Now a substantial portion of the fault voltage will be dropped across the inductor.
For the single phase fault case, the proportion of the fault voltage across the
inductor will be 14.5/(14.5 + 22.4) = 0.393. As before, we need to calculate a target
frequency for the allowable TRV so we can size the TRV shaping capacitor. With
such a high TRV voltage, it no longer makes sense to use the SLF TRV. We will
assume the breakers all passed the C37.06.1 tests for fast TRV.
From Table 3B of C37.06.1-2000 for a 245 kV 63 kA breaker we read for currents 19
kA and below, the Fast TRV has a peak voltage of 487 kV and a time to peak of 30.3
µs. This is a 1-cos TRV so it starts at zero and ½ cycle later is at a peak of 487 kV.
We need the full cycle parameters to use this to get to a target TRV frequency. Thus
the amplitude is 487 kV/2 =243.5 kV. The period is 30.3 x 2 = 60.6 µs. The frequency
is then 1/60.6 µs = .0165 MHz = 16.5 kHz. For our inductor, the peak fault voltage is
200 kV x 0.4 =80 kV. As before, the target TRV frequency is (243.5/80)1/2 x 16.5
kHz = 28.8 kHz. The natural frequency of a 14.5 mH inductor is about 150 kHz,
therefore we will need added capacitance.
As before:
C=
1
=
1
(2πf )2 L (2π × 28800)2 0.0145
= 2.1 nF
(56)
The voltage ratings of the tuning inductor and TRV mitigation capacitor are the
same as for the TLI and its mitigation capacitor:
Tuning inductor 450 kV BIL (minimum)
TRV Mitigation capacitor 900 kV BIL (minimum)
Physical Mounting of the Inductor and TRV mitigation Capacitor
For banks 230kV and below, the most convenient mounting of the inductor and its
parallel TRV mitigation capacitor is on top of the capacitor rack structure. The
capacitor rack and insulators need to be designed to support the weight and wind
loading of these devices.
54